Hydride Length Research Articles

How can machine learning be used for accurate representations and predictions of fracture nucleation in zirconium alloys with hydride populations?

Zirconium alloys are critical material components of systems subjected to harsh environments such as high temperatures, irradiation, and corrosion. When exposed to water in high temperature environments, these alloys can thermo-mechanically degrade by forming hydrides that have a crystalline structure that is different from that of zirconium. Cracks can nucleate near these hydrides; hence, these hydrides are a direct link to fracture failure and overall large inelastic strain deformation modes. To fundamentally understand and predict these microstructural failure modes, we interrogated a finite-element database that was deterministically tailored and generated for large strain-dislocation-density crystalline plasticity and fracture modes. A database of 210 simulations was created to randomly sample from a group of microstructural fingerprints that encompass hydride volume fraction, hydride orientation, grain orientation, hydride length, and hydride spacing for a hydride that is physically representative of an aggregate of a hydride population. Machine learning approaches were then used to understand, identify, and characterize the dominant microstructural mechanisms and characteristics. We first used fat-tailed Cauchy distributions to determine the extreme events. A multilayer perceptron was used to learn the mechanistic characteristics of the material response to predefined strain levels and accurately determine the critical fracture stress response and the accumulated shear slips in critical regions. The predictions indicate that hydride volume fraction, a population-level parameter, had a significant effect on localized parameters, such as fracture stress distribution regions, and on the accumulated immobile dislocation densities both within the face centered cubic hydrides and the hexagonal cubic packed h.c.p. matrix.

Understanding the mechanical integrity of Zircaloy cladding with various radial and circumferential hydride morphologies via image analysis

The mechanical integrity of hydride reoriented reacor-grade Zr-Nb alloy cladding was investigated for various amounts of charged hydrogen and hydride morphologies. The specimens were charged with hydrogen from 0 to 1200 wppm. Hydride reorientation treatment was conducted by applying constant internal pressure (7.5 - 18.5 MPa) to hydrogen-charged cladding tubes subjected to cooling from 400 °C to result in various radial and circumferential hydride fractions. The hydride morphology was examined using optical microscopy. The Radial Hydride Fraction (RHF), Radial Hydride Continuous Path (RHCP), and maximum radial hydride length were obtained using the image analysis software PROPHET. Strain Energy Density (SED) of Zircaloy cladding with various hydride morphologies and concentrations were measured by Ring Compression Tests (RCTs) and analyzed with the results of image analysis. It was found that the RHF gives a strong correlation with the strength of Zircaloy cladding for RHF over 5%. Below 5% of RHF, SED is inversely correlated with the amount of hydrogen. SED exponentially decreased with the maximum hydride length. The fracture mechanics analysis revealed that this behavior supports that radial hydride serves as a critical flaw of hydrided Zircaloy under RCT. And the experimental result demonstrated that circumferential hydrides slightly increase the SED of Zircaloy affected by extensive radial hydride embrittlement by decreasing radial hydride connectivity.

Predictive machine learning approaches for the microstructural behavior of multiphase zirconium alloys

Zirconium alloys are widely used in harsh environments characterized by high temperatures, corrosivity, and radiation exposure. These alloys, which have a hexagonal closed packed (h.c.p.) structure thermo-mechanically degrade, when exposed to severe operating environments due to hydride formation. These hydrides have a different crystalline structure, than the matrix, which results in a multiphase alloy. To accurately model these materials at the relevant physical scale, it is necessary to fully characterize them based on a microstructural fingerprint, which is defined here as a combination of features that include hydride geometry, parent and hydride texture and crystalline structure of these multiphase alloys. Hence, this investigation will develop a reduced order modeling approach, where this microstructural fingerprint is used to predict critical fracture stress levels that are physically consistent with microstructural deformation and fracture modes. Machine Learning (ML) methodologies based on Gaussian Process Regression, random forests, and multilayer perceptrons (MLP) were used to predict material fracture critical stress states. MLPs, or neural networks, had the highest accuracy on held-out test sets across three predetermined strain levels of interest. Hydride orientation, grain orientation or texture, and hydride volume fraction had the greatest effect on critical fracture stress levels and had partial dependencies that were highly significant, and in comparison hydride length and hydride spacing have less effects on fracture stresses. Furthermore, these models were also used accurately predicted material response to nominal applied strains as a function of the microstructural fingerprint.

Modelling the interactions of zirconium hydrides

The zirconium alloys used in the core of nuclear reactors are susceptible to hydride formation and hydrogen embrittlement. Depending on the loading condition, zirconium hydrides usually form in different directions and with various configurations. This paper focuses on the development of the stress fields resulting from the interaction of hydrides, and the subsequent redistribution of hydrogen atoms. The effects of the separation distance between the hydrides formed in parallel and perpendicular configurations are investigated using a coupled diffusion-crystal plasticity finite element approach. The effects of hydride length and width on the stress-assisted diffusion of hydrogen atoms towards hydrides tips are also studied. It is shown that, due to the alignment of growth direction of hydrides, stress fields in the vicinity of two parallel hydrides interact more significantly compared to those of perpendicular hydrides. It is further shown that hydrides with a width of 1 µm propagate faster than those having lower or higher widths.

A novel method for radial hydride analysis in zirconium alloys: HAPPy

Whilst substantial progress has been made in understanding the influence that hydrides have on the mechanical properties of zirconium alloys, there is currently an urgent need for a transparent, reproducible image analysis workflow for their characterisation. In this study, an open-source software package for the analysis of hydride networks, HAPPy (Hydride Analysis Package in Python), is introduced to calculate the radial hydride fraction (RHF) and mean hydride length, as well as characterising the connectivity of the microstructure both quantitatively and qualitatively. In this study, we used the Hough line transform to calculate the orientation distribution of the hydride segments within a micrograph, and its projection on to the radial direction is used to determine the RHF. The proposed methodology is validated, and its robustness is demonstrated over a wide range of microstructures. The image processing prior to analysis as well as the projection method used has been shown to have a significant influence on the calculated RHF, highlighting the need for standardized image analysis workflows to facilitate accurate comparisons and correlations across different studies in the literature. Finally, this paper introduces a new damage susceptibility parameter termed the branch length fraction, which can be used in conjunction with a path of lowest cost algorithm to visualise the most plausible crack path as well as the connectivity evolution over an entire micrograph.

РАСЧЕТНО-ТЕОРЕТИЧЕСКОЕ ИССЛЕДОВАНИЕ МОРФОЛОГИИ ГИДРИДОВ ЦИРКОНИЯ ПРИ СУЩЕСТВЕННО РАЗЛИЧНЫХ СКОРОСТЯХ ОХЛАЖДЕНИЯ

Computation study of the average zirconium hydride length on the cooling rate was performed using the precipitate nucleation and growth model. The cooling rate was varied in the range equal to six orders between typical values for the spent nuclear fuel dry storage conditions to values typical for laboratory tests modeling the dry storage. The calculations showed that as the cooling rate decreases, the hydrides concentration decreases, and their average length increases linearly on a double logarithmic scale. These dependencies have no limit if hydrides were abscended in the sample before the cooling began. If there were hydrides in the sample before the start of cooling, then they will grow and new hydrides will not nucleate in the limit of low cooling rates. For spent nuclear fuel dry storage, these results mean that if hydrides remain in the fuel claddings at the initial storage period, then hydrides morphology and hydrogen embrittlement at the end of the storage period are similar values gained under laboratory conditions with sufficiently slow cooling. If hydrides in fuel claddings are completely dissolved at the beginning of dry storage, then their length will be significantly greater than in laboratory tests at the end of the storage. Therefore, if the threshold values for the circumferential stresses are exceeded in fuel claddings, the hydrogen embrittlement can be expected to be higher than after faster cooling in typical laboratory studies. In this case, the hydrogen embrittlement assessment should be performed in a conservative approach assuming that radial hydrides have an average length equal to the thickness of the fuel cladding.

Analytical approach to DHC description in zirconium alloys

A new model for the threshold stress intensity factor (KIH) for delayed hydride cracking (DHC) has been developed that account for the crack tip stress shielding by hydrides and plastic strains. The article reviews existing approaches to the evaluation of KIH and key features that govern the DHC process: hydride shape and stress field at the crack tip. The evaluation and validation of hydride length and thickness at the crack tip have been carried out. The new parametric model for KIH is based on a direct account for stress concentrator shielding by plastic zone and hydrides at the crack tip. The model results are in good agreement with experimental data.

Quantifying the effect of hydride microstructure on zirconium alloys embrittlement using image analysis

Because hydride microstructure can significantly influence Zr alloy nuclear fuel cladding’s ductility, a new metric has been developed to quantify hydride microstructure in 2D micrographs and relate it to crack propagation. As cladding failure usually results from a hoop stress, this new metric, called the Radial Hydride Continuous Path (RHCP), is based on quantifying the continuity of brittle hydride particles along the radial direction of the cladding tube. Compared to previous metrics, this approach more closely relates to the propensity of a crack to propagate radially through the cladding tube thickness. The RHCP takes into account hydride length, orientation, and connectivity to choose the optimal path for crack propagation through the cladding thickness. The RHCP can therefore be more closely linked to hydride embrittlement of the Zr alloy material, thus creating a relationship between material structure, properties, and performance. The new definition, along with previously proposed metrics such as the Radial Hydride Fraction (RHF), the Hydride Continuity Coefficient (HCC), and the Radial Hydride Continuity Factor (RHCF), have been implemented and automated in MATLAB. These codes are made available with this publication as supplementary materials. These metrics were verified by comparing their predictions of hydride morphology against expected values in simple cases, and the implementation of the new metric was validated by comparing its predictions with manual measurements of hydride microstructure performed on ImageJ. The RHCP was also validated against experimental measurements of fracture behavior and it was shown to correlate with cladding failure better than previous metrics. The information provided by these metrics will help accurately assess cladding integrity during operation, transportation, and storage.

Theory model combined with XFEM of threshold stress intensity factor and critical hydride length for delay hydride cracking

In order to determine the threshold stress intensity factor and critical hydride length for delayed hydride cracking in Zr-2.5Nb pressure tube alloy, the distribution of normal stress in the plastic zone of crack tip by the developed method that combines theory calculation with extended finite element method (XFEM) was improved. The fracture process of two-phase composites containing Zr-2.5Nb and hydride precipitate was simulated by XFEM. Based on that, critical hydride length LC corresponding to the theoretical model for K1H was estimated. Meanwhile, to illustrate the validity of theoretical and numerical methods, recent theoretical models and experimental measurements were utilized to verify the results of this paper. The theoretical model of DHC was improved to estimate the critical hydride length corresponding to threshold stress intensity factor. The predicted value of critical hydride length is close to the experimental values.

Impact of Thermal Tests Simulating Dry Storage of VVER-1000 Fuel on the Hydride Phase Morphology in Fuel Element Claddings

In this work, we carried out metallographic studies of the lateral and longitudinal sections of the fuel element claddings used in the fuel assemblies of VVER-1000 reactors. The average fuel burnup in these fuel elements during one and six annual campaigns was ~20 and ~70 MWd/kg U, respectively. The effect of long-term thermal tests under simulated dry storage conditions of fuel elements on the hydride morphology in the lateral and longitudinal sections of E110 zirconium alloy claddings was experimentally studied. The test fuel elements were kept in helium at 380°C for 468 days under stationary conditions and from 20 to 380°C (48 cycles, holding time from 1 to 10 days at 380°C) for 427 days during thermal cycling. Metallographic studies of the microstructure of the lateral and longitudinal sections of fuel element claddings were carried out in order to determine the effect of fuel burnup and thermal testing modes on the morphology of zirconium hydrides in the fuel elements from the regions corresponding to the middle of the fuel rod and the gas collector location. It was established that the specific length of hydrides does not exceed 4.5 × 10–3 μm–1 and correlates with a low hydrogen content in the claddings. Thermal tests did not change the hydrogen content in the claddings, but caused an increase in the specific length of hydrides in the lateral sections of the claddings by 1.5–1.9 times in fuel elements with low burnup. In the longitudinal sections of the claddings of these fuel elements, as well as in the fuel elements with a high level of fuel burnup, this coagulation of hydrides was not observed. Thermal tests under stationary conditions and in thermal cycling mode did not lead to a significant change in the hydride orientation, which was predominantly tangential with a high fraction of the chaotic component in the lateral section of the claddings, whereas the axial orientation of hydrides prevailed in the longitudinal section.

Hydride Precipitation Behavior with Hydrogen Concentration and Homogenization Temperature in Zr-2.5%Nb Pressure Tube Material

The precipitation characteristics of hydrides in Zr-2.5% Nb pressure tube material were investigated for various hydrogen concentrations and homogenization temperatures. A surface hydride was formed using the electrolytic method and homogenized at various temperatures up to at 550 °C. The homogenization treatment was carried out at 300-550 °C over 240 hours, and the hydrogen concentration in the Zr-2.5% Nb alloy varied from 28 to 144 ppm. Hydrides were observed by optical microscopy and the precipitation parameters of the hydrides were analyzed by MATLAB, quantitatively. This is the first achievement of quantitative analysis of hydrides in Zr-alloys. The length of hydrides increased linearly with hydrogen concentration when homogenized at or below 400 °C. The area fraction of hydrides increased linearly with the hydrogen concentration regardless of homogenization temperature. The length and the ratio (length/thickness) of the hydrides decreased with increasing homogenization temperature at 350-475 °C in 81-86 ppm hydrogen. The changes in the precipitation behavior of the hydrides with homogenization temperature are considered to be due to microstructure changes, both the decomposition of β-Zr and grain growth of α-Zr. Key words: Zr-2.5%Nb alloy, homogenization, hydrogen concentration, hydride, microstructure

Theoretical models of threshold stress intensity factor and critical hydride length for delayed hydride cracking considering thermal stresses

Abstract Delayed hydride cracking (DHC) is an important failure mechanism for Zircaloy tubes in the demanding environment of nuclear reactors. The threshold stress intensity factor, K IH , and critical hydride length, l C , are important parameters to evaluate DHC. Theoretical models of them are developed for Zircaloy tubes undergoing non-homogenous temperature loading, with new stress distributions ahead of the crack tip and thermal stresses involved. A new stress distribution in the plastic zone ahead of the crack tip is proposed according to the fracture mechanics theory of second-order estimate of plastic zone size. The developed models with fewer fitting parameters are validated with the experimental results for K IH and l C . The research results for radial cracking cases indicate that a better agreement for K IH can be achieved; the negative axial thermal stresses can lessen K IH and enlarge the critical hydride length, so its effect should be considered in the safety evaluation and constraint design for fuel rods; the critical hydride length l C changes slightly in a certain range of stress intensity factors, which interprets the phenomenon that the DHC velocity varies slowly in the steady crack growth stage. Besides, the sensitivity analysis of model parameters demonstrates that an increase in yield strength of zircaloy will result in a decrease in the critical hydride length l C , and K IH will firstly decrease and then have a trend to increase with the yield strength of Zircaloy; higher fracture strength of hydrided zircaloy will lead to very high values of threshold stress intensity factor and critical hydride length at higher temperatures, which might be the main mechanism of crack arrest for some Zircaloy materials.

The effect of hydrogen and oxygen contents on hydride reorientations of zirconium alloy cladding tubes

Abstract To investigate the effect of hydrogen and oxygen contents on hydride reorientations during cool-down processes, zirconium–niobium cladding tube specimens were hydrogen-charged before some specimens were oxidized, resulting in 250 ppm and 500 ppm hydrogen-charged specimens containing no oxide and an oxide thickness of 3.8 μm at each surface. The nonoxidized and oxidized hydrogen-charged specimens were heated up to 400°C and then cooled down to room temperature at cooling rates of 0.3°C/min and 8.0°C/min under a tensile hoop stress of 150 MPa. The lower hydrogen contents and the slower cooling rate generated a larger fraction of radial hydrides, a longer radial hydride length, and a lower ultimate tensile strength and plastic elongation. In addition, the oxidized specimens generated a smaller fraction of radial hydrides and a lower ultimate tensile strength and plastic elongation than the nonoxidized specimens. This may be due to: a solubility difference between room temperature and 400°C; an oxygen-induced increase in hydrogen solubility and radial hydride nucleation energy; high temperature residence time during the cool-down; or undissolved circumferential hydrides at 400°C.

Tensile hoop stress-, hydrogen content- and cooling rate-dependent hydride reorientation behaviors of Zr alloy cladding tubes

250ppm hydrogen-charged (250ppm-H) and 500ppm-H Zr alloy cladding tubes oxidized to 2.5μm at their inner and outer surfaces were employed to examine the effect of tensile hoop stress, hydrogen content, cooling rate and oxygen content on the radial hydride precipitation behaviors during cool-down processes. The oxidized cladding tube specimens were heated up to 400°C and then cooled down to room temperature at cooling rates of 0.3, 2.0 or 8.0°C/min under tensile hoop stresses of 80, 100 or 150MPa. The amount of the radial hydrides precipitated and their growth during the cool-down processes were found to be strongly dependent upon the hydrogen content, tensile hoop stress, cooling rate and oxygen content. The lower hydrogen content, the higher tensile hoop stress, the slower cooling rate and the lower oxygen content generated the larger fraction of radial hydrides and the longer radial hydride length. These phenomena may be explained by the solubility difference between room temperature and 400°C, the effect of tensile hoop stress on the radial hydride nucleation energy, cooling-rate-dependent hydrogen super-saturation and high temperature residence time, and the effect of undissolved circumferential hydrides on the radial hydride precipitation.

Cooldown-induced hydride reorientation of hydrogen-charged zirconium alloy cladding tubes

Radial hydride precipitation behaviors of Zr-Nb alloy cladding tubes were investigated using 250 and 500 ppm hydrogen-charged Zr-Nb alloy cladding tubes, cooldown processes from 400 to 300, 200°C and room temperature with five kinds of cooling rates of 0.3, 2.0, 4.0, 7.0 15.0 °C/min under a tensile hoop stress of 150 MPa, which can simulate various cooldown processes during an interim dry storage of PWR nuclear fuel. The slower cooling rate and the lower terminal cooldown temperature generated the more hydrides precipitated during the cooldown as well as the larger fraction and the longer length of radial hydrides. These phenomena can be explained by the difference in the terminal solid solubility of hydrogen for dissolution and precipitation occurring during the heatup and cooldown processes and the cooling rate-dependent hydride nucleation and growth rates. In addition, a drastic decrease in ultimate tensile strength and plastic strain of the tensile tested specimens experiencing the cool-down processes appear to be correlated with the amount of the radial hydrides precipitated during the cooldown.

Cooling rate- and hydrogen content-dependent hydride reorientation and mechanical property degradation of Zr–Nb alloy claddings

As-received, 250ppm and 500ppm hydrogen-charged Zr–Nb alloy cladding tubes were employed to evaluate the effects of cooling rates on the extent of radial hydride formation and mechanical property degradations using the cooling rates of 0.3, 2.0, 4.0 and 15.0°C/min from 400°C to room temperature under a tensile hoop stress of 150MPa, which may simulate a long-term cladding cool-down during an interim dry storage. The hydrogen-charged claddings showed the larger fraction and the longer average length of the radial hydrides with the slower cooling rate. These effects are more dominant for the 250ppm-H cladding tubes than for the 500ppm-H cladding tubes. The cooling rate- and the hydrogen content-dependent radial hydride morphology may be explained by the difference in the remaining circumferential hydride fraction at 400°C and the cooling rate-dependent hydride nucleation and growth rates. The extent of the mechanical property degradations for the hydrogen-charged cladding tubes becomes larger with the decrease of the cooling rate and for the 250ppm-H specimens. These phenomena are well correlated with the cooling rate- and the hydrogen content-dependent radial hydride fraction and length.

Effect of thermo-mechanical cycling on zirconium hydride reorientation studied in situ with synchrotron X-ray diffraction

The circumferential hydrides normally present in nuclear reactor fuel cladding after reactor exposure may dissolve during drying for dry storage and re-precipitate when cooled under load into a more radial orientation, which could embrittle the fuel cladding. It is necessary to study the rates and conditions under which hydride reorientation may happen in order to assess fuel integrity in dry storage. The objective of this work is to study the effect of applied stress and thermal cycling on the hydride morphology in cold-worked stress-relieved Zircaloy-4 by combining conventional metallography and in situ X-ray diffraction techniques. Metallography is used to study the evolution of hydride morphology after several thermo-mechanical cycles. In situ X-ray diffraction performed at the Advanced Photon Source synchrotron provides real-time information on the process of hydride dissolution and precipitation under stress during several thermal cycles. The detailed study of diffracted intensity , peak position and full-width at half-maximum provides information on precipitation kinetics, elastic strains and other characteristics of the hydride precipitation process . The results show that thermo-mechanical cycling significantly increases the radial hydride fraction as well as the hydride length and connectivity. The radial hydrides are observed to precipitate at a lower temperature than circumferential hydrides. Variations in the magnitude and range of hydride strains due to reorientation and cycling have also been observed. These results are discussed in light of existing models and experiments on hydride reorientation. The study of hydride elastic strains during precipitation shows marked differences between circumferential and radial hydrides, which can be used to investigate the reorientation process.

Effect of Hydrides on Mechanical Properties and Failure Morphology of BWR Fuel Cladding at Very High Strain Rate

Abstract The data on the cladding mechanical response under rapid deformation are crucial for the safety assessment of LWR fuel rods for reactivity initiated accident (RIA) and for spent fuel shipping and storage cask-drop accidents. The reported data on the mechanical properties of the irradiated cladding under high strain rates, however, are very limited, and conventional axial tensile data measured at slow strain rates may not be directly applicable to RIA or drop impact analyses. The objective of this work was to obtain basic mechanical properties such as the stress-strain relationship, ductility, and the critical strain energy density (SED) of fuel cladding with various hydride morphologies at high deformation rate. A unique rapid burst test method was employed on open-end tube specimens, achieving a strain rate of ∼1 s−1 and specimen rupture in ∼10 ms. Unirradiated and irradiated Zry-2 fuel cladding specimens were tested from room temperature up to 350°C. The mechanical properties data were assessed in terms of SED and failure strain, and failure morphologies were examined by optical and scanning electron microscopy. The tests performed at room temperature on unirradiated cladding with circumferential hydrides revealed that the failure elongation was unchanged or increased slightly with an increase the in hydrogen content up to ∼100 wt ppm but decreased drastically at ∼400 wt ppm to values approaching 0 %. A drastic reduction in failure strain occurred at a lower hydrogen concentration of ∼100 wt ppm for radial hydrides, compared to ∼200–400 wt ppm for the circumferential hydride distribution. The fraction of specimen thickness occupied by the accumulated length of hydrides in radial direction was a better predictive indicator of specimen failure and ductility reduction than the total hydrogen content. In addition, the high strain rates did not seem to seriously impact stress-strain behavior when hydrogen content is>400 wt ppm. The data analyses revealed smaller values of the strain hardening exponent (n) compared to those from the conventional data for the slow strain rates, indicating that the plastic instability theory simply is not appropriate to evaluate the failure strain under RIA conditions.

Effect of unloading on crack growth rate of Zr–2.5Nb tubes

Crack growth rates (CGRs) of a heat-treated Zr–2.5Nb tube were determined using compact tension specimens with 60 ppm H at 250 °C under the constant and cyclic loads where the load ratio R was changed from 0.13 to 0.68. CGR was the highest under the constant load and decreased under the cyclic load with decreasing R despite a decrease of the critical hydride length indicating the enhanced rate of hydride cracking. Hence, the decreased CGR under the cyclic load is due to unloading during the cyclic load inducing the compressive stress at the crack tip. This compressive stress suppresses hydride nucleation rate, leading it to govern the CGR, according to Kim’s new model. Evidence is provided by citing Simpson’s experiment demonstrating that unloading from 15 MPa √m decreased the CGR of a cold-worked Zr–2.5Nb tube but annealing did the reverse. This study demonstrates for the first time that the retarded CGR due to an overload during the DHC tests is understood in view of crack growth kinetics using Kim’s model.

Kinetics of crack growth in zirconium alloys (II): Stress dependence of the crack growth rate

Delayed hydride cracking tests were conducted on a cold-worked Zr-2.5Nb tube with hydrogen at different test temperatures ranging from 160 to 280 °C in the load increasing mode where an applied KI was increased step-wise by 0.5 MPa m1/2 from 4.5 MPa m1/2. In Stage I with a low KI being close to the threshold stress intensity factor KIH, the striation spacing or the critical hydride length lc that was larger at a lower KI sharply decreased with increasing KI and the crack growth rate (CGR) showed a rapid increase with KI, arising from a reduced hydride cracking rate by creep at a lower KI. In Stage II with KI being much larger than KIH, however, the lc was much smaller and the CGR became independent of KI, demonstrating that the hydride cracking rate becomes so high as to be unaffected by the applied KI, and diffusion-controlled hydride growth becomes a rate-controlling factor for the CGR in Stage II. This explains the constant CGR independent of KI in Stage II. It is demonstrated that the CGR of zirconium alloys is determined by the rate of a slower process between two processes of growth and cracking of hydrides.